Question: Calculate the product below and give your answer in scientific notation. $ {\left(9.5\times 10^{6} \right) \times \left(4.0\times 10^{2} \right) =\ ?} $
Start by collecting the significands and exponents. $ ({9.5} \times {10^{6}}) \times ({4.0} \times {10^{2}}) = ({9.5} \times {4.0}) \times ({10^{6}} \times {10^{2}}) $ Then multiply each term separately. When multiplying exponents with the same base, add the powers together. $= {38.0} \times {10^{6 \,+\, 2}}$ $= {38.0} \times {10^{8}}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$. In this case, we need to move the decimal one position to the left without changing the value of our answer. We can use the fact that ${38.0}$ is the same as ${3.80 \times 10}$ or ${3.80 \times 10^{1}}$. $ = {3.80 \times 10^{1}} \times {10^{8}} $ $ = 3.80 \times 10^{{1} + {8}} $ $= 3.80\times 10^{9}$